Force-Based Methods in Advanced Strength of Materials

A new second-generation force-based method is used to solve statically indeterminate beam bending and the extension, bending, and torsion of frames. To apply the method, it is shown how distributed forces, moments, and torques must be replaced by discrete forces, moments, and torques acting at nodes. Once all the unknown forces, moments, and torques are found, singularity functions are used to describe and plot the internal force, moments, and torques. The second moment area theorem is used to determine the flexibility matrix. The relationship of the force-based method applied in this chapter to a force-based finite element method is also discussed.